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1.Suppose we observe the following relationship between income
and utility for John:
Income/Utility:
20,000
50
25,000
65
27,000
70
30,000
75
35,000
83
40,000
90
a)
Roughly sketch this utility function.
Why does it have this
shape?
b)
Explain in what sense can John be considered riskaverse?
c)
Suppose that John’s current income is $40,000.
The probability
of illness is 0.5, in which case he incurs medical expenses of
$20,000.
What is John’s expected income and expected utility?
d)
What is John’s loss of utility due to this uncertainty?
e)
What is the
maximum premium that John will pay for insurance of $20,000?
f)
What is the actuarially fair premium for John?
Based on (e), what
is John’s risk premium?
g)
Suppose that the premium rate charged
to John is 50 cents for each dollar of coverage.
How much
coverage (what dollar amount) will John buy in this case?
2.
In class, we say that an individual will choose the optimal level
(quantity) of insurance coverage by comparing the marginal
benefits (MB) and the marginal costs (MC) of additional insurance.
Suppose that John is
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 Spring '10
 Ricks
 Utility

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